[Algebra] układ równań
: 2 sty 2012, o 19:07
Niech \(\displaystyle{ -\infty <x_5 \le x_4\le x_3 \le x_2\le x_1<\infty}\) tak że
\(\displaystyle{ \left\{\begin{array}{rcl}x_{1}+x_{2}+x_{3}+x_{4}+x_{5}&=&0\\ x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}&=&1\\ |x_{3}|&=&\sqrt{\frac{2}{15}}\end{array}\right.}\)
Oblicz \(\displaystyle{ x_1-x_5}\).
\(\displaystyle{ \left\{\begin{array}{rcl}x_{1}+x_{2}+x_{3}+x_{4}+x_{5}&=&0\\ x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+x_{5}^{2}&=&1\\ |x_{3}|&=&\sqrt{\frac{2}{15}}\end{array}\right.}\)
Oblicz \(\displaystyle{ x_1-x_5}\).